Finite Group Databasebeta

← #355×D53 #20276391

Subgroups — #355×D53 #20276391

Order 6784.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#124×D53C211yesmaximal, characteristic
2#101×D53C212yesmaximal, complemented
3#16810420C211yesmaximal, characteristic, complemented
4#16810419C212yesmaximal, complemented
5C53×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D53C2211yescharacteristic
7C2×D4×D53C411yescharacteristic
8M16×D53—22no—
9#13133206C2211yescharacteristic
10#13133205C411yescharacteristic
11#13133204C411yescharacteristic
12#13133203—22no—
13C22⋊C4×D53—22no—
14C42×D53C411yescharacteristic
15#13133136C2212yescomplemented
16#13133135—22no—
17#124×C53C2211yescharacteristic
18#101×C53C2212yescomplemented
19C23×D53—21no—
20C2×Q8×C53C2311yescharacteristic
21C2×D4×C53C2×C411yescharacteristic
22C2×C22⋊D53—21no—
23Q8×D53—41no—
24Q8×D53—41no—
25D4×D53—41no—
26D4×D53—41no—
27C2×D212C2×C411yescharacteristic
28C2×C4×D53—21no—
29C2×C4×D53C2×C411yescharacteristic
30C2×C4×D53D412yes—
31C2×Dic106C2×C411yescharacteristic
32C2×Dic106D412yes—
33M16×C53—22no—
34C22⋊C4×C53—22no—
35C42×C53C2×C411yescharacteristic
36C22⋊Dic53—22no—
37#11719921—22no—
38#11719921—22no—
39C4×Dic53—21no—
40C4×Dic53C2×C411yescharacteristic
41#11719917—22no—
42#11719912—42no—
43C8×D53—42no—
44C23×C53—21no—
45C22×D53—21no—
46C22×D53—44no—
47C22×D53—41no—
48C22×D53—41no—
49C22×D53C22⋊C411yescharacteristic
50Q8×C53—41no—
51D4×C53—41no—
52C2×C4×C53—21no—
53C2×C4×C53C22×C411yescharacteristic
54C2×C4×C53C2×D412yes—
55C22⋊D53—42no—
56C2×Dic53—21no—
57C2×Dic53C22⋊C412yes—
58C2×Dic53C22⋊C411yescharacteristic
59D212—41no—
60C4×D53—21no—
61C4×D53—21no—
62C4×D53—22no—
63C4×D53—22no—
64C4×D53—42no—
65Dic106—41no—
66Dic106—42no—
67C8×C53—42no—
68#88322—42no—
69C22×C53—42no—
70C22×C53—41no—
71C22×C53C2×C22⋊C411yescharacteristic
72C2×D53—22no—
73C2×D53—42no—
74C2×D53—41no—
75C2×D53—82no—
76C2×D53—82no—
77C2×D53#9911yescharacteristic
78C2×D53#9911yescharacteristic
79C4×C53—22no—
80C4×C53—21no—
81C4×C53—41no—
82Dic53—22no—
83Dic53—21no—
84Dic53—41no—
85C2×#355—531nomaximal, Sylow
86C2×C53—21no—
87C2×C53—81no—
88C2×C53C2×#9911yescharacteristic
89D53—21no—
90D53—81no—
91D53#35512yesdirect product factor
92C2×#124—531no—
93C2×#101—532no—
94#355—531no—
95#355—532no—
96#355D5311yescharacteristic, direct product factor
97C53C2×#35511yescharacteristic, complemented, Sylow
98C22×Q8—531no—
99C22×D4—531no—
100C2×M16—1062no—
101#124—531no—
102#124—531no—
103#124—531no—
104#124—1062no—
105#124C2×D5311yescharacteristic
106C2×C22⋊C4—1062no—
107C2×C42—531no—
108#101—532no—
109#101—1062no—
110#101C2×D5312yescomplemented
111C24—1061no—
112C2×Q8—531no—
113C2×Q8—532no—
114C2×Q8—2121no—
115C2×Q8—2121no—
116C2×Q8C22×D5311yescharacteristic
117C2×D4—531no—
118C2×D4—1061no—
119C2×D4—2121no—
120C2×D4—2121no—
121C2×D4C4×D5311yescharacteristic
122C22×C4—531no—
123C22×C4—532no—
124C22×C4—1061no—
125M16—22no—
126M16—1062no—
127M16—2122no—
128C2×C8—2122no—
129C22⋊C4—22no—
130C22⋊C4—1062no—
131C22⋊C4—1062no—
132C22⋊C4—1062no—
133C42—531no—
134C42—1061no—
135C42C4×D5311yescharacteristic
136C23—21no—
137C23—531no—
138C23—1061no—
139C23—2121no—
140C23—2121no—
141C23—2124no—
142Q8—41no—
143Q8—2122no—
144Q8—2121no—
145D4—41no—
146D4—2121no—
147D4—2122no—
148C2×C4—21no—
149C2×C4—531no—
150C2×C4—532no—
151C2×C4—1062no—
152C2×C4—1062no—
153C2×C4—1061no—
154C2×C4—1061no—
155C2×C4—1061no—
156C2×C4—2122no—
157C2×C4C2×C4×D5311yescharacteristic
158C2×C4D4×D5312yes—
159C8—42no—
160C8—2122no—
161C22—42no—
162C22—41no—
163C22—531no—
164C22—531no—
165C22—1062no—
166C22—4242no—
167C22—4242no—
168C22—2122no—
169C22—2121no—
170C22C22⋊C4×D5311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—1061no—
175C4—1062no—
176C4—2121no—
177C2—21no—
178C2—81no—
179C2—532no—
180C2—1061no—
181C2—4241no—
182C2#99×D5311yescharacteristic
subgroupG/H
centerC2#99×D53
commutatorC2×C4×C53C22×C4
FrattiniC2×Q8C22×D53
FittingC53×#355C2
socleC2×C53C2×#99
hypercenter#355D53
hypocenterC53C2×#355
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #101×D53C2semidirect
3. #16810420C2semidirect
4. #16810419C2semidirect
5. C53×#355C2semidirect
15. #13133136C22semidirect
18. #101×C53C22semidirect
91. D53#355direct (N × H)
96. #355D53direct (N × H)
97. C53C2×#355semidirect
110. #101C2×D53semidirect